Make a bezier curve into a subdivided mesh?
For subdivide you need quads. Upper face is unsightly ngon and can't be subdivided. Remesh modifier should be helpful in this case.

If Remesh doesn't  do its job well, you can delete ngon and fill area manually with smaller parts by selecting two opposite verts and pres F to fill and press J to connect.

You can combine this procedure with Grid Fill - Ctrl + F > G

I don't know a better solution, I hope someone knows one because this is really good question.